The estimated times and immediate predecessors for the activities in a project at Howard​ Umrah's retinal scanning company are given in the following table. Assume that the activity times are independent.                                                                                                                                                                      Time ​(weeks​) Immediate   Time ​(weeks​) Immediate Activity a m b ​Predecessor(s) Activity a m b ​Predecessor(s) A 8   10   13   — C 9   10   13   A B 4   10   16   — D 6   8   12   B   This exercise contains only parts​ a, b,​ c, and d.   ​a) Based on the activity time​ estimates, the expected times and variance for each of the activities are ​(round your response to two decimal​ places):   Activity Expected Time   Variance A _________   ___________ B ______________   __________ C _______________   ___________ D _______________   ___________   ​b) The expected completion time of the project​ = ____ weeks ​(round your response to two decimal ​places).   ​c) The project variance of completion time​ = ____ weeks ​(round your response to two decimal ​places).   ​d) If the time to complete the project is normally​ distributed, then the probability that the project will be finished in 22 weeks or less​ = _________ ​(enter as a probability and round your response to two decimal​ places). e) If the time to complete the on non crtitical path is normally​ distributed, then the probability that the non crtitical path will be finished in 22 weeks or less​ = _________ ​(enter as a probability and round your response to two decimal​ places).

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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The estimated times and immediate predecessors for the activities in a project at Howard​ Umrah's retinal scanning company are given in the following table. Assume that the activity times are independent.
                                                                                                                                                                  
 
Time
​(weeks​)
Immediate
 
Time
​(weeks​)
Immediate
Activity
a
m
b
​Predecessor(s)
Activity
a
m
b
​Predecessor(s)
A
8
 
10
 
13
 
C
9
 
10
 
13
 
A
B
4
 
10
 
16
 
D
6
 
8
 
12
 
B
 
This exercise contains only parts​ a, b,​ c, and d.
 
​a) Based on the activity time​ estimates, the expected times and variance for each of the activities are ​(round your response to two decimal​ places):
 
Activity
Expected Time
 
Variance
A
_________
 
___________
B
______________
 
__________
C
_______________
 
___________
D
_______________
 
___________
 
​b) The expected completion time of the project​ = ____ weeks ​(round your response to two decimal ​places).
 
​c) The project variance of completion time​ = ____ weeks
​(round your response to two decimal ​places).
 
​d) If the time to complete the project is normally​ distributed, then the probability that the project will be finished in
22 weeks or less​ = _________
​(enter as a probability and round your response to two decimal​ places).
e) If the time to complete the on non crtitical path is normally​ distributed, then the probability that the non crtitical path will be finished in 22 weeks or less​ = _________
​(enter as a probability and round your response to two decimal​ places).
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